Question

1. Incidence of the tax

The supply of fried okra (the tastiest of all foods) is given by the function Q^s = a + bp (with b>0) and its demand is given by Q^d = c + dp (with d<0).

1. What is the equilibrium price of fried okra, p_e⁰?

The government decides to impose a unit tax t on the supply of all food items (supplier pays the tax).

2. What is the equilibrium price after the tax, p_e¹? (Hint: replace p by (p-t) in Q^s)

3. ?_c represents the fraction of the tax absorbed by the consumer, given by ?_c = (p_e¹ – p_e⁰)/t, and ?_p represents the fraction of the tax absorbed by the producer, given by ?_p = (p_e⁰ – p_e¹)/t. Calculate ?_c and ?_p.

4. Suppose b =0.2 and d = - 0.6. Which elasticity is higher (supply or demand)? Calculate ?_c and ?_p.

5. Suppose b =0.4 and d = - 0.1. Which elasticity is higher (supply or demand)? Calculate ?_c and ?_p.

Answer 1

a) at equilibrium, Quantity supplied = Quantity demanded

Therefore, Qs = Qd

= a+bp = c+dp

pe0 = (c-a)/(b-d)....Equilibrium price

b) Since supplier pays the tax, Qs = a+b(p-t)

at equilibrium,

Qs = Qd

a+b(p-t) = c+dp

pe1 = (c-a+bt)/((b-d)......Equilibrium price when supplier pays the tax

c) Substituting the value of pe0 and pe1, we get

(pe1-pe0) = (c-a+bt)/(b-d) - (c-a)/(b-d) = bt/(b-d).............(i)

?_{c =} (pe1 - pe0)/t

= bt/(b-d)*t = b/(b-d)

Therefore, ?_c = b/(b-d)

Since, ?_p = -?_c

we get , ?_{p =} b/(d-b)

d) Since d>b, demand elasticity is higher. Substituting the values of b=.2 and d=-.6, we get

?_c = .2/(.2+.6) = 0.25

.?_p = -0.25